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Titlebook: Coarse Geometry and Randomness; École d’Été de Proba Itai Benjamini Book 2013 Springer International Publishing Switzerland 2013 82B43,82B4

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发表于 2025-3-21 18:38:48 | 显示全部楼层 |阅读模式
书目名称Coarse Geometry and Randomness
副标题École d’Été de Proba
编辑Itai Benjamini
视频videohttp://file.papertrans.cn/229/228715/228715.mp4
概述Includes many exercises of varying difficulty levels.Investigates many open problems.Presents topics not covered by any other book.Includes supplementary material:
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Coarse Geometry and Randomness; École d’Été de Proba Itai Benjamini Book 2013 Springer International Publishing Switzerland 2013 82B43,82B4
描述.These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk..The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ)..
出版日期Book 2013
关键词82B43,82B41,05C81,05C10,05C80; Coarse geometry; Graphs; Percolation; Random walk; Unimodular random graph
版次1
doihttps://doi.org/10.1007/978-3-319-02576-6
isbn_softcover978-3-319-02575-9
isbn_ebook978-3-319-02576-6Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer International Publishing Switzerland 2013
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发表于 2025-3-21 23:08:32 | 显示全部楼层
Book 2013ts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk..The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes
发表于 2025-3-22 01:36:04 | 显示全部楼层
Percolation Perturbations,emerge. When the clusters are subcritical, we see random perturbation of the underling graphs but when the construction is based on critical percolation new type of spaces emerges. More precise definitions appears below. We end with an invariant percolation viewpoint on the incipient infinite cluster (IIC).
发表于 2025-3-22 06:43:35 | 显示全部楼层
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发表于 2025-3-22 16:05:24 | 显示全部楼层
Book 2013of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ)..
发表于 2025-3-22 20:00:31 | 显示全部楼层
发表于 2025-3-23 00:51:54 | 显示全部楼层
Local Limits of Graphs,ous sections. If . = (., .) is such a graph, and ., . ∈ ., the graph distance between . and . in . is defined to be the length of a shortest path in . between . and ., and is denoted by ..(., .). A . graph (., .) is a graph . together with a distinguished vertex . of ..
发表于 2025-3-23 03:09:07 | 显示全部楼层
Uniqueness of the Infinite Percolation Cluster,wer to this question leads to a rather rich landscape with applications in group theory and many still open problems. In this section we study the question of the number of infinite clusters in percolation configurations in the regime . > ...
发表于 2025-3-23 08:14:30 | 显示全部楼层
Percolation Perturbations,sters in the non uniqueness regime on the other hand admit some universal features which are not inherited from the underling graph, they have infinitely many ends and thus are very tree like. When performing the operation of contracting Bernoulli percolation clusters different geometric structures
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